In safety of life applications such as civil air transport, maritime or railroad, each operation has defined integrity requirements. As the term is used herein, “integrity” is the measure of trust that can be placed in the correctness of the information supplied by a navigation system. Integrity parameters include the integrity risk (or probability of hazardously misleading information, PHMI)—the probability that at any moment the true position error exceeds the protection level without an alert. As the term is used herein, a computed “horizontal protection level” is be defined as the radius of a circle in the horizontal plane centered around the true position, which is assured to contain the computed position with specified integrity level. Similarly, a “vertical protection level” is the maximal vertical difference between the true position and the calculated position of a receiver with specified integrity level. When the protection level exceeds an alert limit for a given operation or procedure, there is not enough integrity in the calculated position to perform that procedure. For instance, pilots must then revert to a less stringent one procedure or use a different source of navigation that provides enough integrity. Accordingly, the ability to obtain a low protection level is desired to enable more stringent operations or extend the area where they are available.
The user determines whether integrity monitoring in vertical, horizontal or both directions is required according to the desired procedure. For the sake of clarity only the term protection level is used henceforward to mark either one as the computational considerations are interchangeable.
While monitoring integrity protects the user from excessive position errors, unnecessary warnings may disrupt continuity, i.e. the vehicle's ability to perform its function without an interruption during a procedure. Therefore, probability of false alarms should be upper bounded by the desired value derived from the continuity requirement. False alarms occur when the system raises an alarm about an inconsistency in the measurements even though a fault does not exist in the pseudorange measurements available to the receiver.
One way of monitoring integrity of indicated position of an aircraft in conventional systems is by using what is commonly referred to as the “solution separation method”. The solution separation method is based on computing the difference between a “full-solution” navigation solution that is rendered using all visible satellites (including a quantity of N visible satellites) and a set of navigation “sub-solutions” that are each rendered using a quantity of N−1 visible satellites. In computing the set of navigation sub-solutions, only one satellite fault is assumed at a time, and each “sub-solution” (protecting from some fault mode) is given the same value of false alarm and missed detection probabilities. Then a statistical limit on the separation between the true and the indicated position satisfying both probabilities is computed for each sub-solution and the largest such limit is output as the resultant protection level. When the probability allocations are even, respective limits are unequal due to different covariance of each sub-solution. Consequently, with respect to the resultant protection level (which is larger than or equal to respective limits), individual missed detection probabilities are lower than or equal to those originally intended.
Some conventional systems include receivers equipped with Advanced Receiver Autonomous Integrity Monitoring (ARAIM) for monitoring integrity. ARAIM is based on the solution separation method. For each sufficiently likely fault mode a navigation sub-solution that does not contain the potentially faulty satellites and/or constellations is created. For each sub-solution, a threshold on its fault-free separation from the full solution is created based on its allocation of the whole false alarm budget. The threshold is then compared to the test statistic yielded from actual pseudorange measurements in order to identify a fault. If no fault is present, the protection level is computed as an implicit solution to an equation expressing integrity risk as a function of a protection level and sub-solutions' thresholds, covariances and biases. The equation may conventionally be solved numerically by interval halving. In this way, the protection level is equal to each and every limit and accordingly, the distribution of missed detection probability is optimized.
However, in conventional systems using ARAIM, optimal distribution of the false alarm allocation remains unresolved. Conventional false alarm allocation is even, i.e. each sub-solution's threshold is given the same value. Some conventional systems that have attempted to optimize the allocation of the whole false alarm budget have required significant computational effort in addition to the usual ARAIM load and often does not provide lower protection levels than traditional ARAIM.
For the reasons stated above and for the reasons stated below which will become apparent to those skilled in the art upon reading and understanding the specification, there is a need in the art for improved systems and methods for lowering protection levels by optimal false alarm distribution.